Signal processing in the nervous system?

[chill_factor]

How does body motion control occur? For example, walking on high heels during a strong wind is pretty hard. There is a compressible fluid flow across the body, the center of mass is changing all the time, you have to balance on a tiny surface area, sensor data from the skin, eyes, ears, etc. running into the Gb/s has to be integrated to motor controls... just thinking about it makes it seem complicated.

Is the brain actually doing triple integrals and solving PDEs behind the scenes, or does it have a huge list of control signals to use in case of whatever inputs, or what?

 

[atyy]

Have you seen ?

http://homes.cs.washington.edu/~todorov/papers/optimality_review.pdf is an interesting article.

 

[chill_factor]

quite interesting articles. i have to read them carefully. thanks!

 

[DiracPool]

Is the brain actually doing triple integrals and solving PDEs behind the scenes, or does it have a huge list of control signals to use in case of whatever inputs, or what?

Your looking at a biological organism like a Mitsubishi robot, which is not the way biological nervous systems work. The only thing that does triple integrals is the human mind, not the body. The body is coordinated through vestibular feedback from the semicircular canals in the ear and proprioceptive feedback from the musculature. Most of the adjusting is unconscious and occurs in the spinal cord, midbrain, and basal forebrain, which is why you saw that decerebrate cat able to maintain 3 states of gait.

So again, these are not digital or sequential types of operations of the gigabyte fashion you alluded to. These are not even comparable to parallel distributed computing type of effects. They are fundamentally choatic systems, like the weather. In fact, getting back to the decerebrate cat, those changes in gait, i.e., from standing to walking, and from walking to running, are what we call bifurcations in the chaotic state of the neural pools in the spinal cord and brainstem controlling the motor output. You can actually witness this in EEG or LFP (local field potential) recording of brainstem activity during these transitions, where the global reading change suddenly and abruptly. BTW, although I think we had little other choice in the early days, I'm glad we are not routinely decerabrating cats or even rats anymore for these kinds of studies :)

 

[chill_factor]

Your looking at a biological organism like a Mitsubishi robot, which is not the way biological nervous systems work. The only thing that does triple integrals is the human mind, not the body. The body is coordinated through vestibular feedback from the semicircular canals in the ear and proprioceptive feedback from the musculature. Most of the adjusting is unconscious and occurs in the spinal cord, midbrain, and basal forebrain, which is why you saw that decerebrate cat able to maintain 3 states of gait.

So again, these are not digital or sequential types of operations of the gigabyte fashion you alluded to. These are not even comparable to parallel distributed computing type of effects. They are fundamentally choatic systems, like the weather. In fact, getting back to the decerebrate cat, those changes in gait, i.e., from standing to walking, and from walking to running, are what we call bifurcations in the chaotic state of the neural pools in the spinal cord and brainstem controlling the motor output. You can actually witness this in EEG or LFP (local field potential) recording of brainstem activity during these transitions, where the global reading change suddenly and abruptly. BTW, although I think we had little other choice in the early days, I'm glad we are not routinely decerabrating cats or even rats anymore for these kinds of studies :)

I see. Thank you. I've had a small introduction to chaotic systems in a mechanics class however it was quite basic. Is the state of the brain is an electrical state measured by EEG? Or is it a certain configuration of neurons? Can this state be described by any equation, even in principle, or is fundamentally unable to be described by an equation with a computationally tractable number of terms? I frequently hear about computational neuroscience but don't actually know what they're computing.

 

[DiracPool]

I see. Thank you. I've had a small introduction to chaotic systems in a mechanics class however it was quite basic. Is the state of the brain is an electrical state measured by EEG? Or is it a certain configuration of neurons? Can this state be described by any equation, even in principle, or is fundamentally unable to be described by an equation with a computationally tractable number of terms? I frequently hear about computational neuroscience but don't actually know what they're computing.

The model I work with models information processing in the brain as being manifested through the sequential formation of spatially amplitude modulated "frames" of chaotic states. Instantaneously, you could say that a frame is characterized or defined by the summation of dendritic currents in cortical neuropil, so yes it is directly reflected in EEG tracings, but better represented by LFP incracranial recordings if you have access to those, which you typically don't in humans unless they're undergoing surgery for epilepsy, say.

Mathematically you can model this system using non-linear coupled ODE's, and there are several projects using these sets of equations to simulate brain function right now, along with "percolation" models. Check out the CLION site at the University of Memphis if you want to look into it more

 

[atyy]

@DiracPool: Is chaos established in neural control of the motor system?

For example, it's still undecided if the spontaneous activity of the cortex is chaotic http://www.frontiersin.org/Computational_Neuroscience/10.3389/neuro.10.013.2009/abstract. One of those authors had a proposal for chaos control in a robot http://www.nature.com/news/2010/100117/full/news.2010.15.html, so it's not ruled out either. But is there any consensus?

IIRC, chaos seems very hard to demonstrate experimentally, eg. these reputable authors provided evidence for it in statistical mechanics http://www.nature.com/nature/journal/v394/n6696/abs/394865a0.html, but their claim was controversial http://www.nature.com/nature/journal/v401/n6756/abs/401875a0.html, http://www.nature.com/nature/journal/v401/n6756/abs/401875b0.html,http://www.nature.com/nature/journal/v401/n6756/abs/401876a0.html.

 

[DiracPool]

@DiracPool: Is chaos established in neural control of the motor system?

Well, I think it may be dangerous to state that anything is definitely "established" in network neuroscience. Perhaps I should have said that motoric control systems in living mammals are likey governed through an organized chaotic effect rather than say the simple open loop, feedforward, feedback, or adaptive control systems that traditional robotics uses.

As you point out in your articles, the role of chaotic effects in biological systems is still an active area of research.

From the first article you referenced:

Originally, this dynamical state seemed to be in contradiction
to cortical anatomy, where each neuron receives a huge number
of synapses, typically 10^3–10^4 (Braitenberg and Schüz, 1998): One
might expect that a large number of uncorrelated, or weakly correlated
synaptic inputs to one neuron, given the central limit theorem,
sums up to a regular total input signal with only small relative fluctuations,
therefore excluding the emergence of irregular dynamics.
So the finding of highly irregular activity might be surprising.

My studies build heavily off of Walter Freeman's, who was one of the principle pioneers of the importance of chaotic dynamics in the CNS. He would likely answer the above problem presented by these researchers by saying that the "largely fluctuating membrane potentials
and highly variable inter-spike-intervals" of the individual neurons in question were due to aperiodic competing influences from extra-cortical or intra-cortical inter-areal (in the case of the cortex,) or extra-nuclear (in the case of subcortical regions) afferent pulse volleys. The end result would be the establshment of an aperiodic "ground" attractor, as your authors note, who's effect was not an accidental and unwanted artifact of "sloppy" neuropil organization, but rather a desired property of this tissue designed to prevent the system as a whole from entering a stable, entrained limit cycle state. If the system were to easily enter such low-dimensional states they would lose their flexibility to change those states rapidly and effectively.

In any case, there's too much theory and evidence to go into here and yes, this chaotic dynamical model, which Freeman calls the KV model, is specifically used in modeling cortical behavior, not necessarily motoric control at the level of the brain stem and spinal cord. However, the Carnot engine style formulation of the model he has recently been working on, along with I. Tsuda's concept of "chaotic intenarancy" in the CNS, I think provide a good model for how hierarchically sequenced behavior in mammals manifests from global chaotic behavior in the nervous system. But, of course, more study needs to be done

Here are a few references with more detail on the models I discussed above:
http://www.ncbi.nlm.nih.gov/pubmed/23333569
http://www.ncbi.nlm.nih.gov/pubmed/12239890
http://www.ncbi.nlm.nih.gov/pubmed/19395236

 

[ManFrommars]

Is the state of the brain is an electrical state measured by EEG? Or is it a certain configuration of neurons?

EEG measures the changes in electric potential caused by the coordinated electrical activity of hundreds of thousands, or millions, of neurons. The EEG is a very course-grained measure of the brain's electrical state, but can be very useful as it gives you some idea about the collective behaviour of neuron populations across the surface of the brain. For example, when you close your eyes and relax, the EEG will show a ~10Hz rhythm in the visual cortex.

Can this state be described by any equation, even in principle, or is fundamentally unable to be described by an equation with a computationally tractable number of terms? I frequently hear about computational neuroscience but don't actually know what they're computing.

Given a particular set of EEG measurements, it is very difficult to reconstruct the underlying neural activity (see the MEG inverse problem description on Wikipedia).

You can read a great introduction to computational neuroscience http://briansimulator.org/category/romains-blog/what-is-computational-neuroscience-romains-blog/ - a set of blog posts about the philosophy and methods underlying computational neuroscience. The author makes a distinction between computational and theoretical neuroscience, which is a personal choice as the terms are often used interchangeably, but I think argues his case for this distinction well.

 

[atyy]

@DiracPool, thanks for the references!

I once heard a lecture of Walter Freeman's. Hardly understood a thing - all I remember is something about "intentionality"!

You can read a great introduction to computational neuroscience http://briansimulator.org/category/romains-blog/what-is-computational-neuroscience-romains-blog/ - a set of blog posts about the philosophy and methods underlying computational neuroscience. The author makes a distinction between computational and theoretical neuroscience, which is a personal choice as the terms are often used interchangeably, but I think argues his case for this distinction well.

I too think that's a superb link.